1. Field of the Invention
This invention relates to a data identification method and apparatus which identifies, from within a readout signal from a recording medium on or in which user data are recorded using a recording modulation code called sparse code, the data.
2. Description of the Related Art
Recently, research and development of an information processing apparatus which makes use of the principle of hologram recording are carried out actively as disclosed, for example, in “Holographic encouraged for implementation of a terabyte disk”, Nikkei Electronics, Aug. 15, 2005, No. 906, pp. 51-58 (hereinafter referred to as Non-Patent Document 1).
It is already known that, where hologram recording is used, there is the possibility that a much higher recording density than those of existing optical disks may be achieved. It makes a background of the recent active research and development that peripheral techniques have been and are being prepared such as appearance of light sources such as a semiconductor laser and hologram recording media formed using photopolymer.
As a recording modulation code for hologram recording, a recording modulation code called sparse code wherein m bits from among n bits which form one symbol represent “1” while the remaining n-m bits represent “0” is used favorably. The sparse code is disclosed, for example, in B. M. King and M. A. Neifield, “Sparse modulation coding for increased capacity in volume holographic storage”, APPLIED OPTICS, Vol. 39, pp. 6681-6688, December, 2000 (hereinafter referred to as Non-Patent Document 2).
In the following, the sparse code is described particularly based on quotations from Non-Patent Document 2.
Where the M number which is an index to the overwriting performance of a hologram recording medium is represented by “M#” and the multiplexing number by which the user can actually perform overwriting is represented by “M”, the diffraction efficiency ηpage in a unit of a page is given by the following expression (1):ηpage=(M#/M)^2  (1)
If the ratio of “1s” in a recording modulation code is defined as a sparse rate π1, then in the case of a hologram wherein the number of pixels on one page is “N”, the diffraction efficiency ηpixel in a unit of a pixel is represented by the following expression (2):ηpixel=(M#/M)^2/(π1·N)  (2)
Accordingly, the diffraction efficiency which one pixel can obtain increases as the sparse rate π1 of the recording modulation code decreases.
If it is assumed that noise is fixed irrespective of the multiplexing number, then the number M* of pages which can be multiplexed with a fixed diffraction efficiency η* is given by the following expression (3):M*∝M#/√{square root over ((π1·N))}  (3)
Meanwhile, the information entropy I(π1) of an ideal encoder whose sparse rate is π1 is given, where a sparse rate π0 indicative of the ratio of “0s” of the recording modulation code is used, by the following expression (4-1). Further, the user capacity C by the ideal encoder can be calculated using the following expression (4-2):I(π1)=−π1−log2(π1)−π0·log2(π1)  (4-1)[where π0=1−π1]C=I(π1)·M*  (4-2)
Although the information entropy is a term difficult to understand, this is equivalent to an encoding rate r=k/n of the recording modulation code where user data of k bits are converted into codewords (symbols) of n bits. The information entropy of the ideal encoder corresponds to the encoding rate where n is infinite.
FIG. 17 illustrates a result of calculation of the user capacity C where the sparse rate π1 is varied from 0 to 1.
Since the M number M# may have any particular number, the user capacity is normalized such that it is 1 where the sparse rate π1 is π1=0.5 (the numbers of “1s” and “0s” are equal to each other) with which the information entropy I(π1) is 1.
From this result, it can be recognized that, in hologram recording, the optimum value of the sparse rate π1 is approximately π1=0.25 and the user capacity exhibits an increase by approximately 15% when compared with an alternative case wherein the sparse rate π1 is π1=0.5 where the numbers of “1s” and “0s” are equal to each other.
In an actual recording modulation code, if the bit number n of a codeword is increased, then encoding and decoding become difficult. Therefore, the bit number of a codeword assumes a limited value, and the coding efficient becomes lower than that of the ideal encoder. the sparse code which can be implemented can be defined, using the bit number n of one symbol, the number m of bits of “1” in one symbol and the bit number k of the user, by E(n,m,k). Here, the “symbol” is a minimum unit of a holographic reproduction image composed of, for example, 4×4 pixels, and one symbol corresponds to one codeword (sparse code).
Non-Patent Document 2 discloses a working example wherein a page (sparse page) which is a set of sparse codes is coded in E(52,13,39).
The simplest one of data detection methods is “threshold value detection” wherein a readout signal is identified as “1” if the bit amplitude of the readout signal is greater than a threshold value determined in advance but is identified as “0” if the bit amplitude is smaller than the threshold value. On the other hand, in hologram recording in which the sparse code is used, bit detection methods called “sort detection” and “correlation detection” are used favorably.
In hologram recording, since the variation of the bit amplitude in a page is so great that it is difficult to determine a threshold value for threshold value detection, if the threshold value detection is used, then a very great number of errors appear.
The sort detection is carried out in the following procedure.
First, for example, where the sparse code is E(16,3,8), the bit amplitude of 16-bit codewords (one-symbol codes) which form a readout signal is checked and the numbers #1 to #16 are applied to the bits of the codewords in the descending order of the amplitude.
Then, an identification result is determined such that the codeword bits of the numbers #1 to #3 are set to “1” while the remaining codeword bits of the numbers #4 to #16 are set to “0”.
If it is assumed that the readout signal is in an AD (Analog-to-Digital) converted form in 8 bits (0 to 255), then the correlation detection is performed in the following procedure.
Where the readout signal is in an AD-converted form in 8 bits, since it assumes a value within the range from 0 to 255, it is appropriate to set the value 193 which is ¾ of the distribution of such values as a target value for “1” while the value 64 which is ¼ of the distribution is set as a target value for “0”. Then, for 256 different codewords which may possibly be recorded, at each bit of “1”, the square of the amplitude difference between the target value 191 and the readout signal is calculated, but at each bit of “0”, the square of the amplitude difference between the target value 64 and the readout signal is calculated. Then, the sum of the square errors for 16 bits is calculated to obtain an evaluation value of the likelihood by which each codeword is recorded.
Then, the evaluation values are compared with each other, and that one of the evaluation values which exhibits the highest likelihood is determined as an identification result.
A related method is disclosed also in B. M. King and M. A. Neifield, “Low-complexity maximum-likelihood decoding of shortened enumerative permutation codes for holographic storage”, IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATION, Vol. 19, No. 4, pp. 783-790, April, 2001 (hereinafter referred to as Non-Patent Document 3).